German source Kicker reported earlier on Saturday afternoon that the Gunners had tabled their offer, and the Daily Mail now says that the German club have rejected the offer.
The newspaper claims that Dortmund want at least £53m for Gabon international Aubameyang, and have begun talks with Arsenal about a potential move for Olivier Giroud in the opposite direction.
In a statement, Dortmund CEO Hans-Joachim Watzke said: "I can confirm that there has been a first request from Arsenal for Pierre-Emerick Aubameyang.
"We are not commenting on the sums that have been called from England since noon."
Arsenal are hoping to sign Aubameyang to counteract the probable imminent exit of Chilean Alexis Sanchez to Manchester United.